com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution
Class DoubleExponential4HalfRealLine

java.lang.Object
  com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Substitution
      com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential
          com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential4HalfRealLine

public class DoubleExponential4HalfRealLine
extends DoubleExponential

This Double Exponential transformation is good for the region (0, ∞).

The substitution is

 x = exp(2c sinh(t))
 

The tricky part of using this transformation is to figure out a good range for t. The user should override Substitution.ta() and Substitution.tb() if there is information about the integrand available.

See Also:

Wikipedia: Tanh-sinh quadrature

Field Summary

Fields inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential

a, b, c, f

Fields inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.Substitution

dx, x

Constructor Summary

DoubleExponential4HalfRealLine(UnivariateRealFunction f, double c, double a, double b)
Construct an instance of DoubleExponential4HalfRealLine substitution rule.

Method Summary

Methods inherited from class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.DoubleExponential

ta, tb

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

DoubleExponential4HalfRealLine

public DoubleExponential4HalfRealLine(UnivariateRealFunction f,
                                      double c,
                                      double a,
                                      double b)

Construct an instance of DoubleExponential4HalfRealLine substitution rule.

Parameters:

f - the integrand

c - usually either 0 or 0.5 * PI

a - the lower limit

b - the upper limit